一种基于列生成的定点启发式算法求解服务感知多商品流问题
A column generation-based fixed-point heuristic for the service-aware multi-commodity flow problem
浏览论文内容
中文总结 AI 辅助
研究服务感知多商品流问题，提出基于列生成的迭代定点启发式算法，该算法在求解无弹性MCF和更新需求间交替，实验表明其能快速找到近最优解，比基准方法快且解质量相当。
中文摘要 AI 辅助
我们研究服务感知多商品流（SAMCF）问题，其中需求具有弹性且由逻辑选择模型控制，路由受硬容量约束。在集中式系统最优设置中，网络运营商联合确定服务多少需求以及如何路由。我们将SAMCF制定为非线性规划，并提出一种迭代定点启发式算法，该算法在通过列生成求解无弹性MCF和根据所得服务水平更新需求之间交替进行。基于分段线性需求函数和McCormick包络的两种线性近似作为基准，而需求函数的分段线性外近似用于提供有效的下界。在公共交通实例上的计算实验表明，该启发式算法在不到两秒的时间内找到接近最优的解，比基准方法快几个数量级，同时在十分钟时间限制内能够解决的所有实例上匹配其解质量。
英文摘要
We study the Service-Aware Multi-Commodity Flow (SAMCF) problem, in which demand is elastic and governed by a logit choice model while routing is subject to hard capacity constraints. In a centralized, system-optimal setting, the network operator jointly determines how much demand to serve and how to route it. We formulate the SAMCF as a nonlinear program and propose an iterative fixed-point heuristic that alternates between solving an inelastic MCF via column generation and updating demand from the resulting service levels. Two linear approximations based on piecewise-linear demand functions and McCormick envelopes serve as benchmarks, while a piecewise-linear outer-approximation of the demand function is used to provide valid lower bounds. Computational experiments on public transport instances show that the heuristic finds near-optimal solutions in under two seconds - orders of magnitude faster than the benchmark methods - while matching their solution quality on all instances they can solve within a ten-minute time limit.
